Having said that though, this will probably just inflame things further. As Fabius Maximus remarks, bin Laden was holed up in the mountains and his leadership was quite erratic. With bin Laden as a martyr and possibly better leadership, Al Qaeda might be more of a threat in the coming years, not less.
Like Maximus, I also found the over-use of "I" in Obama's speech jarring:
And so shortly after taking office, I directed Leon Panetta, the director of the CIA, to make the killing or capture of bin Laden the top priority of our war against al Qaeda. Even as we continued our broader efforts to disrupt, dismantle and defeat his network. Then last August, after years of painstaking work by our intelligence community, I was briefed on a possible lead to bin Laden. It was far from certain. And it took many months to run this thread to ground. I met repeatedly with my national security team as we developed more information about the possibility that we had located bin Laden hiding within a compound deep inside Pakistan. And finally, last week, I determined that we had enough intelligence to take action and authorized an operation to get Osama bin Laden and bring him to justice. Today, at my direction, the United States launched a targeted operation against that compound in Abad Abad, Pakistan. A small team of Americans carried out the operation with extraordinary courage and capability. No Americans were harmed. They took care to avoid civilian casualties.
Obama should have stepped back a bit, had the military dump bin Laden's body into the sea and then maintained radio silence. Studied ambiguity would have been better for the longer term.
As much as it pains me to say this, Bush's speech on capturing Saddam Hussein was much more a model of probity. Notice the complete lack of "I did this", "I did that" there in Bush's speech. The only use of first person is about bringing messages to the Iraqi people and to the American people. A messenger, not a principal player.